报告题目 (Title)：On a coupled Kadomtsev-Petviashvili system associated with an elliptic curve （关于一个与椭圆曲线相关的耦合KP系统）
报告人 (Speaker)：傅蔚 副教授（华东师范大学）
报告时间 (Time)：2023年06月06日 16:00-17:00
报告地点 (Place)：校本部乐乎楼海纳厅
邀请人(Inviter)：张大军 教授
主办部门：理学院数学系
报告摘要：
The coupled Kadomtsev-Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766-771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more insights into the integrability of this elliptic model from the perspective of a general linear integral equation. As a result, we successfully construct for the elliptic coupled Kadomtsev-Petviashvili system not only a Lax pair composed of differential operators in $2\times2$ matrix form but also multi-soliton solutions with phases parametrised by points on the elliptic curve. Dimensional reductions based on the direct linearisation, to the elliptic coupled Korteweg-de Vries and Boussinesq systems, are also discussed. In addition, a novel class of solutions are obtained for the $D_\infty$-type Kadomtsev-Petviashvili equation with nonzero constant background as a byproduct.
